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This is the only book actuaries need to understand generalized linear models (GLMs) for insurance applications. GLMs are used in the insurance industry to support critical decisions. Until now, no text has introduced GLMs in this context or addressed the problems specific to insurance data. Using insurance data sets, this practical, rigorous book treats GLMs, covers all standard exponential family distributions, extends the methodology to correlated data structures, and discusses recent developments which go beyond the GLM. The issues in the book are specific to insurance data, such as model selection in the presence of large data sets and the handling of varying exposure times. Exercises and data-based practicals help readers to consolidate their skills, with solutions and data sets given on the companion website. Although the book is package-independent, SAS code and output examples feature in an appendix and on the website. In addition, R code and output for all the examples are provided on the website.
Insurance --- -Linear models (Statistics) --- -368.01 --- Models, Linear (Statistics) --- Mathematical models --- Mathematical statistics --- Statistics --- Assurance (Insurance) --- Coverage, Insurance --- Indemnity insurance --- Insurance coverage --- Insurance industry --- Insurance protection --- Mutual insurance --- Underwriting --- Finance --- Mathematics --- -Electronic information resources --- Electronic information resources --- E-books --- Linear models (Statistics) --- Business mathematics --- Actuarial science --- Mathematics. --- Models lineals (Estadística) --- Assegurances --- Models matemàtics. --- Matemàtica. --- Mathematical Sciences --- Probability --- Càlcul actuarial --- Ciència actuarial --- Matemàtica actuarial --- Matemàtica financera --- Finances --- Finances privades --- Estadística --- Estadística matemàtica --- Models matemàtics
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An emerging field in statistics, distributional regression facilitates the modelling of the complete conditional distribution, rather than just the mean. This book introduces generalized additive models for location, scale and shape (GAMLSS) - one of the most important classes of distributional regression. Taking a broad perspective, the authors consider penalized likelihood inference, Bayesian inference, and boosting as potential ways of estimating models and illustrate their usage in complex applications. Written by the international team who developed GAMLSS, the text's focus on practical questions and problems sets it apart. Case studies demonstrate how researchers in statistics and other data-rich disciplines can use the model in their work, exploring examples ranging from fetal ultrasounds to social media performance metrics. The R code and data sets for the case studies are available on the book's companion website, allowing for replication and further study.
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